In our post on Intro to Factors, we showed how Fama and French added value (HML) and small-caps (SMB) to the original market-risk model to account for the relative out-performance of small-cap/value investment strategies. The genesis of their idea was basically that certain portfolio returns deviated significantly from the market-risk-only model and they wanted to see if they could account for it systematically.
In 2014, they updated their model by adding 2 more factors: profitability (RWM) and investment (CMA) – stocks with a high operating profitability perform better and stocks of companies with the high total asset growth have below average returns.
No Free Lunch
Investors can construct long-only portfolios with a single leg of any one of these factors to exploit it.
For example, one can rank stocks by high book-to-price ratio, take the first 100 of them and create a value portfolio. Such a portfolio will have a high factor loading (ß) for HML.
But just because you can do something like this, should you do it? Depends on your motivations. Factor returns ebb and flow. To visualize the cumulative effect of their spreads, you can plot them as a return series:
As you can see, single factors can spend years in negative territory. During that time, plain-old, low-cost market-beta would be racing ahead while a factor portfolio will be an expensive drag.
This leads us to posit that single factor portfolios are not buy-and-hold-forever investments. For example, during the final phases of a bull market, everything is expensive. So a portfolio of “pure value” stocks will be basically junk that no investor cares about. If you were to invest in such a portfolio, then when the market turns, these stocks are likely to drawdown way more than the rest of the market. If they were unloved in a bull, they will be massacred at the turn.
So unless you thoroughly understand the dynamics of how different factors behave in different market environments, you should stick to market beta.
The Factor Zoo
Fama and French opened the flood-gates for factor research. Academics rushed to discover and publish increasingly esoteric and often overlapping factors. At last count, there were over 400 factors published in various academic journals.
While some of them are a result of p-hacking and not all of them result in lasting alpha, there are a couple that have confounded academics and practitioners alike with their persistence: momentum and low-volatility.
Two economists walk down a road and they see a twenty dollar bill lying on the side-walk. One of them asks “is that a twenty dollar bill?” Then the other one answers “It can’t be, because someone would have picked it up already,” and they keep walking. (source)
In 1965, Eugene Fama published his dissertation arguing for the random walk hypothesis. i.e., stock market prices evolve according to a random walk (so price changes are random) and thus cannot be predicted. This was followed by Paul Samuelson, who published a proof showing that if the market is efficient, prices will exhibit random-walk behavior. (source)
Together, they form the basis of the efficient market hypothesis (EMH).
The efficient market hypothesis (EMH), is a hypothesis that states that share prices reflect all information and consistent alpha generation is impossible. According to the EMH, stocks always trade at their fair value on exchanges, making it impossible for investors to purchase undervalued stocks or sell stocks for inflated prices. Therefore, it should be impossible to outperform the overall market through expert stock selection or market timing, and the only way an investor can obtain higher returns is by purchasing riskier investments. (source)
Inefficiencies are opportunities
Any market practitioner knows that this is not entirely true. There are numerous hurdles in the way of pure efficiency:
Information is not free.
Liquidity is not unlimited.
Prices are not continuous.
Market statistics are forever in flux.
Investors have different goals and pursue different outcomes.
Taxes, rules and regulations.
According to EMH, a portfolio’s return could be fully explained by the market (source):
r = rf+ ß(rm – rf) + α
Where:
r = Expected rate of return
rf = Risk-free rate
ß= Beta
(rm – rf)= Market risk premium
This is a single-factor model. i.e., portfolio returns are only explained by market risk (rm – rf: market risk premium.) Whatever cannot be explained by the market is α, or the portfolio manager’s skill.
However, if you setup a portfolio in certain ways, you consistently ended up with higher returns, implying that there was something about the market, something systematic, that was not being captured by this equation. So, if you were rewarding a portfolio manager only on the basis of α calculated from the above equation, then you were probably over-paying the PM for harvesting something that the market offered for “free.”
In 1992, Eugene Fama and Kenneth French designed a model to fix this – the Fama–French three-factor model.
The Fama-French model aims to describe stock returns through three factors: (1) market risk (rm – rf: market risk premium,) (2) the outperformance of small-cap companies relative to large-cap companies (SMB: Small Minus Big,) and (3) the outperformance of high book-to-market value companies versus low book-to-market value companies (HML: High Minus Low.) The rationale behind the model is that high value and small-cap companies tend to regularly outperform the overall market. (source)
Where:
r= Expected rate of return
rf = Risk-free rate
ß = Factor’s coefficient (sensitivity)
(rm – rf)= Market risk premium
SMB(Small Minus Big) = Historic excess returns of small-cap companies over large-cap companies
HML(High Minus Low) = Historic excess returns of value stocks (high book-to-price ratio) over growth stocks (low book-to-price ratio)
↋= Risk, or α
Think of SMB and HML as “base-rates.” A portfolio’s returns can now be explained by the degree of tilt (factor cofficients, ßs) it has towards value (HML) and small-caps (SMB). Furthermore, you can set up incentives for the portfolio manager that incorporates these factors so that he is rewarded only if he can out-perform a generic small-cap/value portfolio.
The academic definition of value (HML) and small-caps (SMB) is quite different from what investors are used to colloquially. Fama and French were interested in the decomposition of portfolio returns into sub-components (factors) and the persistence of these factors over many years/decades. They did this by constructing SMB and HML as long-short portfolios and analyzing the spread. It is very different from what the media refers to by these terms. It is useful to think of these as spreads and not as typical long-only “value” portfolio.
No pain, No gain
Just because these factors are persistent, doesn’t mean that they are always positive. A simple way to visualize this is to see the cumulative returns of the market risk premium (MKT = rm – rf) over SMB and HML.
There are periods of both out-performance and under-performance. In fact, one of the theories proposed to explain the persistence of these factors is behavioral: investors herd into value or small-caps based on recent out-performance. Thus, setting them up for subsequent under-performance. Upon which, they will exit en masse, allowing the factors to out-perform once again.
The real world is messy
Most investors are long-only. Whey we buy a value fund, for example, we are not really buying a Fama-French HML long-short portfolio. Our portfolios have a market beta and a bunch of other things affecting it besides high book-to-price ratio.
To visualize this, if we decompose the iShares Russell 1000 Value ETF, IWD, to its 3-factors, we get:
rf + 0.92*(rm – rf) –0.06*SMB +0.35*HML + α
Compared to iShares Russell 1000 Growth ETF, IWF:
rf + 1.03*(rm – rf) –0.05*SMB –0.27*HML + α
Conclusion
The Fama-French 3-Factor model is a useful tool to analyze investment portfolios. It allows us to decompose returns to different factors so that we can better understand the drivers of returns.
Years of returns can get wiped out in a month in the markets. While investors mostly focus on the average, the tails end up dictating their actual returns. (Introduction)
Sampling and Measurement
Typically, a uniform sample is taken. The problem with this is it under-represents the tails. This leads to models that work on average but blow up on occasion. One way to overcome this problem is through stratified sampling. (Sampling)
Expected shortfall (ES) is a risk measure that can be used to estimate the loss during tail-events. (Measuring)
Acceptance
All assets have fat tails. It is a feature, not a bug. (Historical)
There is no asset free of extreme tail losses. If an asset produces any sort of return, it is going to be exposed to some sort of tail event.
One can try to find uncorrelated assets so that those losses don’t occur at the same time. However, correlations between asset returns are not stable – they change over time and behave quite erratically during market panics.
In the end, to be an investor is to accept the fact that large losses occasionally happen.
No matter how you slice it, there is no escaping tail events in investing. It is the nature of the beast and every attempt you make eliminating the risk results in you giving up a significant portion of your returns. But given two investment opportunities, how do you go about figuring out which one is more susceptible to tail events?
Expected shortfall (ES) is a risk measure that can be used to estimate the loss during tail-events. The “expected shortfall at q% level” is the expected return on the portfolio in the worst q% of cases. ES estimates the risk of an investment in a conservative way, focusing on the less profitable outcomes. For high values of q it ignores the most profitable but unlikely possibilities, while for small values of q it focuses on the worst losses. Typically q is 5% and in formulae, p (= 100% – q) is often used as a substitute.
ES of Weekly Returns
Here’s a dilemma that most investors face: Mid-caps have given higher returns in the past compared to large-caps. But, how do their tail-risks compare?
Turns out, ES of the NIFTY MIDCAP 150 TR index is -6.73% vs. NIFTY 50 TR’s -5.65%. This is how much an investor would have lost in the worst 5% of weeks since 2011.
Sampling
In our previous post, we showed how strata-sampling can be used to make sure that you don’t end up ignoring tail-risk in your simulations. By definition, tail-events are rare. So, the differences are subtle.
Tactical Allocation
Reducing tail-risk is one of the biggest draws of tactical allocation. Anything that reduces deep drawdowns has the effect of keeping investors faithful to their investment process.
One way to setup a tactical allocation strategy is to use a Simple Moving Average (SMA) to decide between equity and bond allocations. Different SMA look-back periods will result in different levels of risk and reward. From an ES point of view, here’s how things for NIFTY shakes out:
Since 1999
Since 2010
Using an SMA and re-balancing weekly significantly reduces tail-risk.
How far back should you go?
The problem with tail-events is that there aren’t enough of them to build an effective model. There’s always a temptation to use as much data as possible so that these events find sufficient representation. However, markets evolve, regulatory structures change and past data stop being representative.
For example, if you run a tactical allocation back-test with all the data that is available, you’ll conclude that shorter the SMA, the better:
However, if you remove 2008 and its aftermath and look only are the data from 2011 onward, you get a different picture:
While metrics like ES and strategies like SMA are useful, the data that they are presented will give different results based on the regime that they are drawn from.
Risk management is a continuous process and cannot be reduced to single number.
